For the following exercise, determine whether the ordered pair is a solution to the system of equations. 3 x − y = 4 x + 4 y = − 3 and ( − 1 , 1 )

Question

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Answer 1

Textbook Question

Chapter 7, Problem 1RE

For the following exercise, determine whether the ordered pair is a solution to the system of equations.

3 x − y = 4

x + 4 y = − 3 and ( − 1 , 1 )

Expert Solution & Answer

To determine

To Check:

Whether the given ordered pair is a solution of the system.

Explanation of Solution

Given information:

3x−y=4 ; x+4y=−3with (−1,1)

Concept Involved:

Solving a system of equation means finding the value of (x, y) which will make both the equation TRUE.

Here in this problem to check whether the given point is solution of system of equation, we need to substitute the value of x and y given into system of equation, and check whether it makes both the equation TRUE.

If and only if given point (x, y) makes both the equation TRUE, graphically (x, y) will be point were the two given lines MEET and it is called a solution of system of equation.

There are different types of solution for system of equation.

Case 1: When we get intersecting lines, the solution of system of equations is UNIQUE and it is the point where the graphs intersect. The solution set in interval notation is given by {(x,y)}. The solution is described as consistent and independent. Also for intersecting lines, the slope of the system of equations will be DIFFERENT.

Case 2: When we get coinciding lines, the solution of system of equations is INFINITE because the lines meet at numerous points. The solution is represented as {x∈ℜ,y∈ℜ}

The solution is described as consistent and dependent. Also for intersecting lines, the slope and y-intercept of the system of equations will be SAME.

Case 3: When we have parallel lines, the solution of the system of equations is NO SOLUTION because the lines will never meet. The solution is represented as {}or ∅. The system of equation hence described as inconsistent. Also for parallel lines, both slope and y-intercept of the equation will be DIFFERENT.

Calculation:

Description	3x−y=4 ; x+4y=−3with (−1,1)
Step 1: Let us label the system of equations as 1^s^tand 2ⁿ^dequation	{3x−y=4→ 1stequationx+4y=−3 →2ndequation
Step 2: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 1^s^tand check whether it is TRUE or FALSE.	3x−y=43(−1)−1=4⇒−3−1=4−4=4FALSE
Step 3: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 2ⁿ^dand check whether it is TRUE or FALSE.	x+4y=−3−1+4(1)=−3⇒−1+4=−33=−3FALSE
Step 4: Since the ordered pair (−1,1) makes 1^s^tequationFALSE and 2ⁿ^dequation FALSE, it is the solution of the given system of equation	(−1,1)is a Solution to the below system of equation {3x−y=4→ 1stequationx+4y=−3 →2ndequation

Conclusion:

The ordered pair (−1,1)makes both 1^s^tand 2ⁿ^dequation FALSE; it is the not a solution of the given system of equation.

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Answer 2

Textbook Question

Chapter 7, Problem 1RE

For the following exercise, determine whether the ordered pair is a solution to the system of equations.

3 x − y = 4

x + 4 y = − 3 and ( − 1 , 1 )

Expert Solution & Answer

To determine

To Check:

Whether the given ordered pair is a solution of the system.

Explanation of Solution

Given information:

3x−y=4 ; x+4y=−3with (−1,1)

Concept Involved:

Solving a system of equation means finding the value of (x, y) which will make both the equation TRUE.

Here in this problem to check whether the given point is solution of system of equation, we need to substitute the value of x and y given into system of equation, and check whether it makes both the equation TRUE.

If and only if given point (x, y) makes both the equation TRUE, graphically (x, y) will be point were the two given lines MEET and it is called a solution of system of equation.

There are different types of solution for system of equation.

Case 1: When we get intersecting lines, the solution of system of equations is UNIQUE and it is the point where the graphs intersect. The solution set in interval notation is given by {(x,y)}. The solution is described as consistent and independent. Also for intersecting lines, the slope of the system of equations will be DIFFERENT.

Case 2: When we get coinciding lines, the solution of system of equations is INFINITE because the lines meet at numerous points. The solution is represented as {x∈ℜ,y∈ℜ}

The solution is described as consistent and dependent. Also for intersecting lines, the slope and y-intercept of the system of equations will be SAME.

Case 3: When we have parallel lines, the solution of the system of equations is NO SOLUTION because the lines will never meet. The solution is represented as {}or ∅. The system of equation hence described as inconsistent. Also for parallel lines, both slope and y-intercept of the equation will be DIFFERENT.

Calculation:

Description	3x−y=4 ; x+4y=−3with (−1,1)
Step 1: Let us label the system of equations as 1^s^tand 2ⁿ^dequation	{3x−y=4→ 1stequationx+4y=−3 →2ndequation
Step 2: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 1^s^tand check whether it is TRUE or FALSE.	3x−y=43(−1)−1=4⇒−3−1=4−4=4FALSE
Step 3: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 2ⁿ^dand check whether it is TRUE or FALSE.	x+4y=−3−1+4(1)=−3⇒−1+4=−33=−3FALSE
Step 4: Since the ordered pair (−1,1) makes 1^s^tequationFALSE and 2ⁿ^dequation FALSE, it is the solution of the given system of equation	(−1,1)is a Solution to the below system of equation {3x−y=4→ 1stequationx+4y=−3 →2ndequation

Conclusion:

The ordered pair (−1,1)makes both 1^s^tand 2ⁿ^dequation FALSE; it is the not a solution of the given system of equation.

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Answer 3

Textbook Question

Chapter 7, Problem 1RE

For the following exercise, determine whether the ordered pair is a solution to the system of equations.

3 x − y = 4

x + 4 y = − 3 and ( − 1 , 1 )

Expert Solution & Answer

To determine

To Check:

Whether the given ordered pair is a solution of the system.

Explanation of Solution

Given information:

3x−y=4 ; x+4y=−3with (−1,1)

Concept Involved:

Solving a system of equation means finding the value of (x, y) which will make both the equation TRUE.

Here in this problem to check whether the given point is solution of system of equation, we need to substitute the value of x and y given into system of equation, and check whether it makes both the equation TRUE.

If and only if given point (x, y) makes both the equation TRUE, graphically (x, y) will be point were the two given lines MEET and it is called a solution of system of equation.

There are different types of solution for system of equation.

Case 1: When we get intersecting lines, the solution of system of equations is UNIQUE and it is the point where the graphs intersect. The solution set in interval notation is given by {(x,y)}. The solution is described as consistent and independent. Also for intersecting lines, the slope of the system of equations will be DIFFERENT.

Case 2: When we get coinciding lines, the solution of system of equations is INFINITE because the lines meet at numerous points. The solution is represented as {x∈ℜ,y∈ℜ}

The solution is described as consistent and dependent. Also for intersecting lines, the slope and y-intercept of the system of equations will be SAME.

Case 3: When we have parallel lines, the solution of the system of equations is NO SOLUTION because the lines will never meet. The solution is represented as {}or ∅. The system of equation hence described as inconsistent. Also for parallel lines, both slope and y-intercept of the equation will be DIFFERENT.

Calculation:

Description	3x−y=4 ; x+4y=−3with (−1,1)
Step 1: Let us label the system of equations as 1^s^tand 2ⁿ^dequation	{3x−y=4→ 1stequationx+4y=−3 →2ndequation
Step 2: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 1^s^tand check whether it is TRUE or FALSE.	3x−y=43(−1)−1=4⇒−3−1=4−4=4FALSE
Step 3: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 2ⁿ^dand check whether it is TRUE or FALSE.	x+4y=−3−1+4(1)=−3⇒−1+4=−33=−3FALSE
Step 4: Since the ordered pair (−1,1) makes 1^s^tequationFALSE and 2ⁿ^dequation FALSE, it is the solution of the given system of equation	(−1,1)is a Solution to the below system of equation {3x−y=4→ 1stequationx+4y=−3 →2ndequation

Conclusion:

The ordered pair (−1,1)makes both 1^s^tand 2ⁿ^dequation FALSE; it is the not a solution of the given system of equation.

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Answer 4

Textbook Question

Chapter 7, Problem 1RE

For the following exercise, determine whether the ordered pair is a solution to the system of equations.

3 x − y = 4

x + 4 y = − 3 and ( − 1 , 1 )

Expert Solution & Answer

To determine

To Check:

Whether the given ordered pair is a solution of the system.

Explanation of Solution

Given information:

3x−y=4 ; x+4y=−3with (−1,1)

Concept Involved:

Solving a system of equation means finding the value of (x, y) which will make both the equation TRUE.

Here in this problem to check whether the given point is solution of system of equation, we need to substitute the value of x and y given into system of equation, and check whether it makes both the equation TRUE.

If and only if given point (x, y) makes both the equation TRUE, graphically (x, y) will be point were the two given lines MEET and it is called a solution of system of equation.

There are different types of solution for system of equation.

Case 1: When we get intersecting lines, the solution of system of equations is UNIQUE and it is the point where the graphs intersect. The solution set in interval notation is given by {(x,y)}. The solution is described as consistent and independent. Also for intersecting lines, the slope of the system of equations will be DIFFERENT.

Case 2: When we get coinciding lines, the solution of system of equations is INFINITE because the lines meet at numerous points. The solution is represented as {x∈ℜ,y∈ℜ}

The solution is described as consistent and dependent. Also for intersecting lines, the slope and y-intercept of the system of equations will be SAME.

Case 3: When we have parallel lines, the solution of the system of equations is NO SOLUTION because the lines will never meet. The solution is represented as {}or ∅. The system of equation hence described as inconsistent. Also for parallel lines, both slope and y-intercept of the equation will be DIFFERENT.

Calculation:

Description	3x−y=4 ; x+4y=−3with (−1,1)
Step 1: Let us label the system of equations as 1^s^tand 2ⁿ^dequation	{3x−y=4→ 1stequationx+4y=−3 →2ndequation
Step 2: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 1^s^tand check whether it is TRUE or FALSE.	3x−y=43(−1)−1=4⇒−3−1=4−4=4FALSE
Step 3: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 2ⁿ^dand check whether it is TRUE or FALSE.	x+4y=−3−1+4(1)=−3⇒−1+4=−33=−3FALSE
Step 4: Since the ordered pair (−1,1) makes 1^s^tequationFALSE and 2ⁿ^dequation FALSE, it is the solution of the given system of equation	(−1,1)is a Solution to the below system of equation {3x−y=4→ 1stequationx+4y=−3 →2ndequation

Conclusion:

The ordered pair (−1,1)makes both 1^s^tand 2ⁿ^dequation FALSE; it is the not a solution of the given system of equation.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

To Check:

Whether the given ordered pair is a solution of the system.

Explanation of Solution

Given information:

3x−y=4 ; x+4y=−3with (−1,1)

Concept Involved:

Solving a system of equation means finding the value of (x, y) which will make both the equation TRUE.

Here in this problem to check whether the given point is solution of system of equation, we need to substitute the value of x and y given into system of equation, and check whether it makes both the equation TRUE.

If and only if given point (x, y) makes both the equation TRUE, graphically (x, y) will be point were the two given lines MEET and it is called a solution of system of equation.

There are different types of solution for system of equation.

Case 1: When we get intersecting lines, the solution of system of equations is UNIQUE and it is the point where the graphs intersect. The solution set in interval notation is given by {(x,y)}. The solution is described as consistent and independent. Also for intersecting lines, the slope of the system of equations will be DIFFERENT.

Case 2: When we get coinciding lines, the solution of system of equations is INFINITE because the lines meet at numerous points. The solution is represented as {x∈ℜ,y∈ℜ}

The solution is described as consistent and dependent. Also for intersecting lines, the slope and y-intercept of the system of equations will be SAME.

Case 3: When we have parallel lines, the solution of the system of equations is NO SOLUTION because the lines will never meet. The solution is represented as {}or ∅. The system of equation hence described as inconsistent. Also for parallel lines, both slope and y-intercept of the equation will be DIFFERENT.

Calculation:

Description	3x−y=4 ; x+4y=−3with (−1,1)
Step 1: Let us label the system of equations as 1^s^tand 2ⁿ^dequation	{3x−y=4→ 1stequationx+4y=−3 →2ndequation
Step 2: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 1^s^tand check whether it is TRUE or FALSE.	3x−y=43(−1)−1=4⇒−3−1=4−4=4FALSE
Step 3: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 2ⁿ^dand check whether it is TRUE or FALSE.	x+4y=−3−1+4(1)=−3⇒−1+4=−33=−3FALSE
Step 4: Since the ordered pair (−1,1) makes 1^s^tequationFALSE and 2ⁿ^dequation FALSE, it is the solution of the given system of equation	(−1,1)is a Solution to the below system of equation {3x−y=4→ 1stequationx+4y=−3 →2ndequation

Conclusion:

The ordered pair (−1,1)makes both 1^s^tand 2ⁿ^dequation FALSE; it is the not a solution of the given system of equation.

Answer 8

Expert Solution & Answer

To determine

To Check:

Whether the given ordered pair is a solution of the system.

Explanation of Solution

Given information:

3x−y=4 ; x+4y=−3with (−1,1)

Concept Involved:

Solving a system of equation means finding the value of (x, y) which will make both the equation TRUE.

Here in this problem to check whether the given point is solution of system of equation, we need to substitute the value of x and y given into system of equation, and check whether it makes both the equation TRUE.

If and only if given point (x, y) makes both the equation TRUE, graphically (x, y) will be point were the two given lines MEET and it is called a solution of system of equation.

There are different types of solution for system of equation.

Case 1: When we get intersecting lines, the solution of system of equations is UNIQUE and it is the point where the graphs intersect. The solution set in interval notation is given by {(x,y)}. The solution is described as consistent and independent. Also for intersecting lines, the slope of the system of equations will be DIFFERENT.

Case 2: When we get coinciding lines, the solution of system of equations is INFINITE because the lines meet at numerous points. The solution is represented as {x∈ℜ,y∈ℜ}

The solution is described as consistent and dependent. Also for intersecting lines, the slope and y-intercept of the system of equations will be SAME.

Case 3: When we have parallel lines, the solution of the system of equations is NO SOLUTION because the lines will never meet. The solution is represented as {}or ∅. The system of equation hence described as inconsistent. Also for parallel lines, both slope and y-intercept of the equation will be DIFFERENT.

Calculation:

Description	3x−y=4 ; x+4y=−3with (−1,1)
Step 1: Let us label the system of equations as 1^s^tand 2ⁿ^dequation	{3x−y=4→ 1stequationx+4y=−3 →2ndequation
Step 2: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 1^s^tand check whether it is TRUE or FALSE.	3x−y=43(−1)−1=4⇒−3−1=4−4=4FALSE
Step 3: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 2ⁿ^dand check whether it is TRUE or FALSE.	x+4y=−3−1+4(1)=−3⇒−1+4=−33=−3FALSE
Step 4: Since the ordered pair (−1,1) makes 1^s^tequationFALSE and 2ⁿ^dequation FALSE, it is the solution of the given system of equation	(−1,1)is a Solution to the below system of equation {3x−y=4→ 1stequationx+4y=−3 →2ndequation

Conclusion:

The ordered pair (−1,1)makes both 1^s^tand 2ⁿ^dequation FALSE; it is the not a solution of the given system of equation.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

To Check:

Whether the given ordered pair is a solution of the system.

Answer 12

Explanation of Solution

Given information:

3x−y=4 ; x+4y=−3with (−1,1)

Concept Involved:

Solving a system of equation means finding the value of (x, y) which will make both the equation TRUE.

Here in this problem to check whether the given point is solution of system of equation, we need to substitute the value of x and y given into system of equation, and check whether it makes both the equation TRUE.

If and only if given point (x, y) makes both the equation TRUE, graphically (x, y) will be point were the two given lines MEET and it is called a solution of system of equation.

There are different types of solution for system of equation.

Case 1: When we get intersecting lines, the solution of system of equations is UNIQUE and it is the point where the graphs intersect. The solution set in interval notation is given by {(x,y)}. The solution is described as consistent and independent. Also for intersecting lines, the slope of the system of equations will be DIFFERENT.

Case 2: When we get coinciding lines, the solution of system of equations is INFINITE because the lines meet at numerous points. The solution is represented as {x∈ℜ,y∈ℜ}

The solution is described as consistent and dependent. Also for intersecting lines, the slope and y-intercept of the system of equations will be SAME.

Case 3: When we have parallel lines, the solution of the system of equations is NO SOLUTION because the lines will never meet. The solution is represented as {}or ∅. The system of equation hence described as inconsistent. Also for parallel lines, both slope and y-intercept of the equation will be DIFFERENT.

Calculation:

Description	3x−y=4 ; x+4y=−3with (−1,1)
Step 1: Let us label the system of equations as 1^s^tand 2ⁿ^dequation	{3x−y=4→ 1stequationx+4y=−3 →2ndequation
Step 2: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 1^s^tand check whether it is TRUE or FALSE.	3x−y=43(−1)−1=4⇒−3−1=4−4=4FALSE
Step 3: In an attempt of checking whether the given ordered pair (−1,1) is solution to the system of equation by Substituting x=−1, y=1 in 2ⁿ^dand check whether it is TRUE or FALSE.	x+4y=−3−1+4(1)=−3⇒−1+4=−33=−3FALSE
Step 4: Since the ordered pair (−1,1) makes 1^s^tequationFALSE and 2ⁿ^dequation FALSE, it is the solution of the given system of equation	(−1,1)is a Solution to the below system of equation {3x−y=4→ 1stequationx+4y=−3 →2ndequation